MinT - Best Known (46, 46+49, s)-Nets in Base 4

Best Known (46, 46+49, s)-Nets in Base 4

(46, 46+49, 56)-Net over F₄ — Constructive and digital

Digital (46, 95, 56)-net over F₄, using

t-expansion [i] based on digital (33, 95, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(46, 46+49, 65)-Net in Base 4 — Constructive

(46, 95, 65)-net in base 4, using

1 times m-reduction [i] based on (46, 96, 65)-net in base 4, using
- base change [i] based on digital (14, 64, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(46, 46+49, 81)-Net over F₄ — Digital

Digital (46, 95, 81)-net over F₄, using

net from sequence [i] based on digital (46, 80)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 46 and N(F) ≥ 81, using
  - Drinfeld modules of rank 1 [i]

(46, 46+49, 725)-Net in Base 4 — Upper bound on s

There is no (46, 95, 726)-net in base 4, because

1 times m-reduction [i] would yield (46, 94, 726)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 392 856482 243966 800271 378815 988790 657027 732933 900231 709576 > 4⁹⁴ [i]